A theoretical model suggests that a mechanically induced twist of the soft body underlies the formation of helicospiral shells in snails and ammonites and also accounts for the startling and unique meandering shells observed in certain species. This theory addresses fundamental developmental issues of chirality and symmetry breaking: in the case of ammonites, how a bilaterally symmetric body can sometimes secrete a nonsymmetric shell; for gastropods, how an intrinsic twist possibly due to the asymmetric development of musculature can provide a mechanical motor for generating a chiral shell. Our model highlights the importance of physical forces in biological development and sheds light on shell coiling in snails, which have been used for a century as model organisms in genetic research.